Question

There are a total of 105 foreign language students in a high school where they offer Spanish, French, and German. There are 18 students who take at least 2 languages at once (the size of the three double intersections added together). If there are 42 Spanish students, 40 French students, and 41 German students, how many students take all three languages at once?

Answer 1

None take all 3 languages

Step-by-step explanation:

I take the number of students who at least take 2 languages and by comparing with the different possibilities make the operation.

Let 18 take spanish and french

Then 42-18=24 take only spanish

40-18=22 take only french

41 take only German

18+24+22+41=105

None take all 3 languages